Bivariance, Grothendieck duality and Hochschild homology I: Construction of a bivariant theory
نویسندگان
چکیده
منابع مشابه
, Duality and D - Branes in Bivariant K - Theory
We describe a categorical framework for the classification of D-branes on noncommutative spaces using techniques from bivariant K-theory of C∗-algebras. We present a new description of bivariant K-theory in terms of noncommutative correspondences which is nicely adapted to the study of T-duality in open string theory. We systematically use the diagram calculus for bivariant K-theory as detailed...
متن کاملSymplectic Homology as Hochschild Homology
In the wake of Donaldson’s pioneering work [6], Picard-Lefschetz theory has been extended from its original context in algebraic geometry to (a very large class of) symplectic manifolds. Informally speaking, one can view the theory as analogous to Kirby calculus: one of its basic insights is that one can give a (non-unique) presentation of a symplectic manifold, in terms of a symplectic hypersu...
متن کاملHarrison Homology, Hochschild Homology and Triples*l
We consider the following situation: a field k, a commutative k-algebra R and a left R-module M. Since R is commutative, M may also be considered as an R-R bimodule with the same operation on each side (such modules are often termed symmetric). With these assumptions we have the Harrison (co-) homology groups Harr,(R, M) (Harr*(R, M)), the Hochschild (co-) homology groups Hoch, (R, M) (Hoch*(R,...
متن کاملHomological Perturbation Theory Hochschild Homology and Formal Groups
As Don Schack mentioned in his plenary talk [SDS], Gerstenhaber [MG] observed that if A is an associative algebra, then the Hochschild cohomology of A is a graded commutative algebra with an additional structure, viz., that of a Lie algebra. The two structures satisfy a compatibility condition (graded Poission structure). We agree to call such structures G–algebras (Gerstenhaber–algebras). Scha...
متن کاملOn the topological Hochschild homology of bu. I
The purpose of this paper and its sequel is to determine the homotopy groups of the spectrum THH(`). Here p is an odd prime, ` is the Adams summand of p-local connective K-theory (see for example [25]) and THH is the topological Hochschild homology construction introduced by Bökstedt in [3]. In the present paper we will determine the mod p homotopy groups of THH(`) and also the integral homotop...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Asian Journal of Mathematics
سال: 2011
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2011.v15.n3.a7